Information Spreading on Almost Torus Networks

TL;DR

This paper analyzes how information spreads in almost torus networks, a variation of torus networks with some nodes or edges removed, using spectral properties to estimate spreading dynamics.

Contribution

It provides explicit formulas for the characteristic polynomial and spectral radius of almost torus networks, enabling better understanding of information dissemination.

Findings

Derived explicit expressions for the characteristic polynomial.

Established tight lower bounds for spectral radius computation.

Estimated information spreading dynamics on almost torus networks.

Abstract

Epidemic modeling has been extensively used in the last years in the field of telecommunications and computer networks. We consider the popular Susceptible-Infected-Susceptible spreading model as the metric for information spreading. In this work, we analyze information spreading on a particular class of networks denoted almost torus networks and over the lattice which can be considered as the limit when the torus length goes to infinity. Almost torus networks consist on the torus network topology where some nodes or edges have been removed. We find explicit expressions for the characteristic polynomial of these graphs and tight lower bounds for its computation. These expressions allow us to estimate their spectral radius and thus how the information spreads on these networks.